{"title":"Integrability of Series with Respect to Multiplicative Systems and Generalized Derivatives","authors":"N. Yu. Agafonova, S. S. Volosivets","doi":"10.3103/s1066369x24700142","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We give some necessary and sufficient conditiosn for the convergence of generalized derivatives of sums of series with respect to multiplicative systems and the corresponding Fourier series. These conditions are counterparts of trigonometric results of S. Sheng, W.O. Bray, and Č.V. Stanojević and extend some results of F. Móricz proved for Walsh–Fourier series.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"30 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s1066369x24700142","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We give some necessary and sufficient conditiosn for the convergence of generalized derivatives of sums of series with respect to multiplicative systems and the corresponding Fourier series. These conditions are counterparts of trigonometric results of S. Sheng, W.O. Bray, and Č.V. Stanojević and extend some results of F. Móricz proved for Walsh–Fourier series.
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